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Ore condition
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(Definition)
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A ring $R$ satisfies the left Ore condition (resp. right Ore condition) if and only if for all elements $x$ and $y$ with $x$ regular, there exist elements $u$ and $v$ with $v$ regular such that $$ux = vy \quad\text{(resp.} xu = yv\text{).}$$
A ring which satisfies the (left, right) Ore condition is called a (left, right) Ore ring.
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"Ore condition" is owned by mclase.
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Cross-references: right, regular, ring
There is 1 reference to this entry.
This is version 3 of Ore condition, born on 2003-10-20, modified 2003-11-21.
Object id is 5403, canonical name is OreCondition.
Accessed 8275 times total.
Classification:
| AMS MSC: | 16U20 (Associative rings and algebras :: Conditions on elements :: Ore rings, multiplicative sets, Ore localization) |
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Pending Errata and Addenda
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